This research uses mathematical and computational techniques to determine the functional properties of local-circuit neurons, based on the well-founded results of cable theory, compartmental analysis, and biophysics of ionic fluxes across nerve-cell membranes. Four specific problem areas are addressed: (1) functional roles of dendritic spines, (2) nonspiking neurons and reciprocal synapses, (3) mathematical characterization of neuronal excitability, and (4) cellular mechanisms of neuronal plasticity. The aim of these studies is to provide realistic, quantiative, and consistent data for the behavior of these systems so that both experimental and theoretical investigations can be rigorously based on solid theory. Applications of experimental findings in local-circuit neurons to larger neural systems and to clinical problems will be strengthened and made more reliable by these extensive computational investigations.